ODE
\[ 2 (1-x) x y''(x)+(1-2 x) y'(x)+8 y(x)=0 \] ODE Classification
[_Jacobi, [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.183189 (sec), leaf count = 35
\[\left \{\left \{y(x)\to c_1 \left (8 x^2-8 x+1\right )+c_2 \sin \left (4 \sin ^{-1}\left (\sqrt {1-x}\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.061 (sec), leaf count = 31
\[\left [y \left (x \right ) = \textit {\_C1} \left (8 x^{2}-8 x +1\right )+\textit {\_C2} \left (-1+2 x \right ) \sqrt {x \left (x -1\right )}\right ]\] Mathematica raw input
DSolve[8*y[x] + (1 - 2*x)*y'[x] + 2*(1 - x)*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (1 - 8*x + 8*x^2)*C[1] + C[2]*Sin[4*ArcSin[Sqrt[1 - x]]]}}
Maple raw input
dsolve(2*x*(1-x)*diff(diff(y(x),x),x)+(1-2*x)*diff(y(x),x)+8*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*(8*x^2-8*x+1)+_C2*(-1+2*x)*(x*(x-1))^(1/2)]